## wp1759 - 2. The Model8 ## Source details **Canonical URL:** [wp1759 - 2. The Model8](https://www.imf.org/-/media/files/publications/wp/2017/wp1759.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2017/wp1759.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2017/wp1759.pdf.json) --- ### Model architecture and agents - Economy: infinite-horizon with two agent types (entrepreneurs = borrowers; households = savers) and capital producers supplying new capital goods. - Entrepreneurs: - Production: Cobb-Douglas Y_t = k_t^μ l_t^{1−μ} with depreciation rate δ. - Preferences: maximize E_0 Σ_{t=0}^∞ γ^t ln c_t (γ is the entrepreneurial discount factor). - Flow of funds (equation (2)): k_t^μ l_t^{1−μ} + b_t + q_t(1−δ)k_t = c_t + q_t k_{t+1} + R_{t−1} b_{t−1} + w_t l_t. - Collateral constraint (equation (3)): b_t ≤ (1/z) q_t k_t R_t (z = value of capital collateral required per unit of loan). - First-order conditions: - Consumption Euler: 1/c_t = E_t[γ R_t / c_{t+1}] + λ_t R_t. (4) - Labor demand: w_t l_t = (1−μ) y_t. (5) - Capital demand: 1/(c_t q_t) = E_t[γ/c_{t+1} (μ y_{t+1}/k_t + q_{t+1}(1−δ))] + λ_t q_t (1/z). (6) - λ_t = Lagrange multiplier on the borrowing constraint. - Households: - Preferences: maximize E_0 Σ_{t=0}^∞ β^t [ln c'_t − (1/η) l_t^η] with β > γ. - Flow of funds (equation (8)): c'_t + b'_t = R_{t−1} b'_{t−1} + w_t l_t. - First-order conditions: - Euler: 1/c'_t = β E_t[R_t / c'_{t+1}]. (9) - Labor supply: w_t = c'_t l_t^{η−1}. (10) - Capital producers: - Investment i_t with adjustment costs ⇒ decreasing marginal return to investment. - Price of capital condition (equation (12)): q_t = [1 − φ (i_t/k_t − δ)]^{−1}. ### Markets and equilibrium - Goods market clearing (13): Y_t = c_t + c'_t + i_t. - Financial market clearing (14): b_t + b'_t = 0. - Capital accumulation (15): k_{t+1} = [i_t/k_t − φ/2 (i_t/k_t − δ)^2] k_t + (1−δ) k_t. ### Macroprudential instrument and policy alternatives - Instrument: collateral requirement z (value of capital collateral required per unit of loan). - Policy implementations compared: - Active policy: time-varying rule where collateral requirements respond to deviations of credit from its steady state (countercyclical). - Informational scenarios: - Complete information: policymaker observes indicators accurately and without lag. - Incomplete information: policymakers observe indicators with noise and lag. - Passive policy: permanently increased collateral requirements (time-invariant tightening). ### Welfare measurement and evaluation methodology - Numerical welfare evaluation via second-order approximation to the equilibrium (Schmitt-Grohe and Uribe (2004) methodology). - Individual welfare: - Borrowers: W_t ≡ E_t Σ_{m=0}^∞ γ^m log c_{t+m}. (16) - Savers: W'_t ≡ E_t Σ_{m=0}^∞ β^m [log c'_{t+m} − (l_{t+m})^η / η]. (17) - Social welfare: weighted sum of individual welfare where each agent’s welfare is weighted by her discount factor (following Mendicino and Pescatori (2007)). - Welfare in consumption-equivalent units: - CE = exp[(1−γ)(W_P − W^*)]^{−1}. (18) - CE'_0 = exp[(1−β)(W_P − W'^*)]^{−1}. (19) - Positive CE indicates a welfare gain relative to the baseline (policy not active). - Passive policy assessed with both stochastic (second-order) and deterministic models to separate volatility effects from steady-state changes. ### Key model equations and notation preserved - Preserve equations (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14), (15), (16), (17), (18), (19) as presented above. --- ### 2.6 Macroprudential Policy Alternatives — Active Policy (Rule) and Passive Policy - Active Policy: Collateral requirement rule (complete information form): - z_t = z_SS * (E_t b_{t+1} / b_SS)^{φ_b} (equation (B1) described in text) - z_SS = steady-state collateral requirement. - φ_b ≥ 0 measures response to expected deviations of credit from steady state. - Policy is countercyclical; implementation does not change the steady state when information is complete. - Active Policy: Incomplete information specification: - Policymaker observes credit with a lag of four quarters and with error: b_{t-4} = e b_{t-4} + x_t. - Operational rule used: - z_t = z_SS * [ (b_{t-4} - x_t) / b_SS ]^{φ_b} (equation (20) described in text) - Noise: x_t = ρ_x x_{t-1} + v_t (AR(1); equation (21)); v_t ~ i.i.d. N(0, σ_v^2) - Key risk: noisy and lagged data can trigger unwarranted or ineffective policy responses and introduce further volatility. - Passive Policy: - Definition: permanent change in z as a non–time-varying macroprudential instrument. - Simpler for LIDCs due to lower data and capacity requirements. - Macro implication: changes the economy’s steady state (permanent restriction of credit) and implies a long-run output cost. ### Dynamic properties — Benchmark calibration (Table 1 values) - β Discount Factor Households: 0.99 - γ Discount Factor Entrepreneurs: 0.98 - z Collateral Requirement: 183.2 - δ Capital depreciation: 0.03 - μ Capital Share: 0.35 - η Labor supply: 3 - ρ Shock persistence: 0.8 - Notes: - Collateral benchmark from World Bank Enterprise Survey Data: in Sub-Saharan Africa the value of collateral needed for a loan is 183.2%. - Household discount factor 0.99 (annualized interest ≈ 4%). - Entrepreneur discount factor slightly lower to make collateral constraint binding. - Demand shock: additive shock t in Euler equation; log(t) follows AR(1) with persistence 0.80. ### Impulse response setup and example calibrations - Comparative cases: benchmark (no macroprudential), active rule with complete information, passive policy calibrated to match average increase implied by active rule. - Active rule reaction parameter used in presentation: φ_b = 0.5 (complete information). - Passive calibration: take average increase of z implied by active rule for first 20 periods and approximate a permanent equivalent increase. - Example textual approximation: benchmark collateral requirement 183.2 increases to approximately 250 in the passive calibration. ### Qualitative impulse-response results to a positive demand shock - Active rule (complete information): - Collateral requirements increase temporarily and return to steady state. - Cuts borrowing more strongly than passive rule; mitigates expansion in entrepreneurial consumption. - Household consumption increases less (they save less due to credit cut). - Interest rate decreases more with the macroprudential tool. - No long-run output cost (steady state of output unchanged). - Passive rule: - Collateral requirement increases permanently, compresses credit, reduces steady-state credit and output (long-run output cost). - Benchmark (no macroprudential): - Collateral requirement remains at steady-state level 183.2 through the shock. --- ### Macroeconomic and financial effects — Active vs. Passive, information problems - Active Policy with Complete Information — effect of φ_b on financial stability: - Metric: standard deviation of borrowing as proxy for financial stability. - Larger φ_b reduces borrowing volatility, but marginal gains diminish at high φ_b. - Numerical examples: - φ_b = 100 → standard deviation of borrowing = 0.423537 - φ_b = 1000 → standard deviation of borrowing = 0.421284 - Paper choice: φ_b = 0.5 as conservative value. - Active Policy with Incomplete Information — lagged and noisy data effects: - Noise benchmark: 1% shock in data noise with 0.8 persistence. - Three incomplete-information cases: (i) lag, (ii) noise, (iii) lag + noise. - Main findings: - Very low φ_b ⇒ results under complete and incomplete information are similar. - Aggressive φ_b effective under complete information can be counterproductive under incomplete information and increase credit volatility. - Lag alone: rule performs marginally worse than complete information. - Noise alone: rule is less effective and can worsen financial stability versus complete information. - Lag + noise: exacerbates instability; with large φ_b the regulator can generate more instability than the no-policy case. - Cautious rule benchmark: φ_b = 0.1 yields limited adverse effects under incomplete information. - Conclusion: incomplete information can reverse stabilizing effects of an active rule if the rule is aggressive; caution and lower φ_b reduce risk. - Passive Policy — financial stability tradeoff: - Passive policy damps short-term credit dynamics but reduces steady-state credit and output (long-run output cost). - To obtain the same financial stability as the active rule (complete information), the collateral requirement must be raised permanently to 833 percent, which would imply: - steady-state output = 1.74 - an output loss of 5.1 percent --- ### 4.3 Passive Policy — Mechanisms, distributional and welfare effects - Overview: - Passive policy implemented as a permanent increase in the collateral requirement (tightens collateral constraint permanently). - Intended effect: reduce volatility of borrowing; unintended effect: reduce steady-state credit and output permanently. - Financial stability effects: - Initial calibrated collateral: 183.2%. - Empirical textual result: "When collateral requirements increase, the standard deviation of credit decreases–a passive macroprudential policy is able to achieve a higher financial stability." - Matching active-rule stability requires passive z = 833 percent (see above), with steady-state output = 1.74 and output loss = 5.1 percent. - Steady-state and distributional effects: - Permanent increase in collateral ⇒ lower steady-state output; reduced access to finance for entrepreneurs ⇒ lower borrowing and production in steady state. - Entrepreneurs’ steady-state consumption falls relative to households; gap widens under passive policy. - Gini coefficient increases with higher collateral requirements: "As collateral requirements increase, the Gini coe¢cient becomes larger, meaning that inequality goes up." - Simplified Gini used: if high income group is u% of population and earns fraction f% of income, then Gini = f − u. - Proportion of entrepreneurs adjusted to match initial Gini close to average in LIDCs. - Welfare implications (stochastic vs deterministic decomposition): - Entrepreneurs: benefit from increased financial stability (lower consumption volatility) when collateral requirement increases. - Savers (households): worse off with passive policy because they bear long-run output cost. - Aggregate welfare: stochastic-model aggregate welfare is positive for some passive-policy parameter values; deterministic (steady-state) decomposition shows entrepreneurs worse off and households slightly better off — aggregate welfare slightly increasing due to redistribution. - Comparison with active policy under incomplete information: - Active policy with complete, timely, accurate information preferred — lower variability without steady-state cost. - Active policy with incomplete information can be welfare-decreasing and generate higher volatility. - A cautious active rule (φ_b = 0.1) or a passive approach may be preferable under noisy/lagged data despite long-run output and distributional costs. - For the "cautious rule," the active rule is preferred to the passive rule up to a collateral requirement of approximately 312 percent. - Quantitative caveat: "Quantitative results should be taken with some caution since the rule is not optimally implemented and the value of the noise is not calibrated to a specific case." ### Selected quantitative statistics (from Tables and text) - Table 2 (Volatilities and steady states; columns: Benchmark | Active (Complete Inf ) | Active (Incomplete Inf ) | Passive) - σ_b: 6.31 | 2.91 | 13.72 | 5.15 - σ_y: 2.69 | 1.72 | 3.56 | 2.17 - b_SS: 8.75 | 8.75 | 8.75 | 6.03 - y_SS: 1.83 | 1.83 | 1.83 | 1.80 - Active-rule numerical examples and choices: - φ_b values discussed: 0.5 (presentation choice), 0.1 (cautious rule), 100, 1000 (numerical examples for marginal gains). - φ_b = 100 → standard deviation of borrowing = 0.423537 - φ_b = 1000 → standard deviation of borrowing = 0.421284 - Passive-policy illustrative statistics: - To match active-rule financial stability → passive collateral requirement = 833 percent → steady-state output = 1.74 → output loss = 5.1 percent. - Table 3 (Welfare and inequality; columns: Benchmark | Active (Complete) | Active (Incomplete) | Passive) - Welfare gain: -0.38 | -0.99 | 0.22 | (passive column as presented in source) - c_SS (entrepreneur consumption steady state): 0.19 | 0.19 | 0.19 | 0.15 - c0_SS (household consumption steady state): 6.34 | 6.34 | 6.34 | 6.53 - Gini: 0.46 | 0.46 | 0.46 | 0.48 --- ### Policy trade-offs and recommendations (from model results) - Trade-offs: - Passive policy: improves financial stability (lower credit volatility) but imposes a permanent steady-state output cost and raises inequality by reducing entrepreneurs’ consumption disproportionately. - Active policy (complete information): preferred — achieves lower volatility without steady-state cost. - Active policy (incomplete information): can be counterproductive — higher volatility and welfare losses if the rule is aggressive. - Recommendations for LIDCs: - Be cautious adopting passive macroprudential tools as first-best due to long-run output, inequality, and welfare implications that may outweigh stability benefits. - Prioritize reducing data and capacity problems, and improving policy framework and implementation to enable effective use of time-varying (active) macroprudential approaches. - As data and monitoring improve, consider less aggressive responses to financial sector developments. *Source: wp1759 - 2. The Model8; 2.6 Macroprudential Policy Alternatives; 4.3 Passive Policy (IMF Working Paper).* ### 2. The Model8 ### wp1759 - 2. The Model8 ### Model architecture and agents - Infinite-horizon economy with two agent types: entrepreneurs (borrowers) and households (savers); capital producers supply new capital goods. - Entrepreneurs: - Production: Cobb-Douglas Y_t = k_t^μ l_t^{1−μ} with capital depreciation rate δ. - Preferences: maximize E_0 Σ_{t=0}^∞ γ^t ln c_t where γ is the entrepreneurial discount factor. - Flow of funds (equation (2)): k_t^μ l_t^{1−μ} + b_t + q_t(1−δ)k_t = c_t + q_t k_{t+1} + R_{t−1} b_{t−1} + w_t l_t. - Collateral constraint (equation (3)): b_t ≤ (1/z) q_t k_t R_t where z is the value of capital collateral required per unit of loan. - First-order conditions: - Consumption Euler: 1/c_t = E_t[γ R_t / c_{t+1}] + λ_t R_t. (4) - Labor demand: w_t l_t = (1−μ) y_t. (5) - Capital demand: 1/(c_t q_t) = E_t[γ/c_{t+1} (μ y_{t+1}/k_t + q_{t+1}(1−δ))] + λ_t q_t (1/z). (6) - λ_t denotes the Lagrange multiplier on the borrowing constraint. - Households: - Preferences: maximize E_0 Σ_{t=0}^∞ β^t [ln c'_t − (1/η) l_t^η] where β is the household discount factor (β > γ). - Flow of funds (equation (8)): c'_t + b'_t = R_{t−1} b'_{t−1} + w_t l_t. - First-order conditions: - Euler: 1/c'_t = β E_t[R_t / c'_{t+1}]. (9) - Labor supply: w_t = c'_t l_t^{η−1}. (10) - Capital producers: - Investment i_t used as input; adjustment costs imply decreasing marginal return to investment. - Profit maximization yields price of capital condition (equation (12)): q_t = [1 − φ (i_t/k_t − δ)]^{−1}. ### Markets and equilibrium - Goods market clearing (13): Y_t = c_t + c'_t + i_t. - Financial market clearing (14): b_t + b'_t = 0. - Capital accumulation (15): k_{t+1} = [i_t/k_t − φ/2 (i_t/k_t − δ)^2] k_t + (1−δ) k_t. ### Macroprudential instrument and policy alternatives - Macroprudential instrument: the collateral requirement z (value of capital collateral required per unit of loan). - Policy implementations compared: - Active policy: time-varying rule in which collateral requirements respond to deviations of credit from its steady state (countercyclical). - Two informational scenarios: - Complete information: macroprudential policymaker observes economic/financial indicators accurately and without lag. - Incomplete information: policymakers observe indicators with noise and lag (data and capacity limitations approximated by absence of complete information). - Passive policy: permanently increased collateral requirements (time-invariant tightening). ### Welfare measurement and evaluation methodology - Welfare evaluated numerically via second-order approximation to the equilibrium for a given policy and then computing welfare using that solution (as in Schmitt-Grohe and Uribe (2004)). - Individual welfare definitions: - Borrowers: W_t ≡ E_t Σ_{m=0}^∞ γ^m log c_{t+m}. (16) - Savers: W'_t ≡ E_t Σ_{m=0}^∞ β^m [log c'_{t+m} − (l_{t+m})^η / η]. (17) - Social welfare (following Mendicino and Pescatori (2007)) is a weighted sum of individual welfare where each agent’s welfare is weighted by her discount factor. - Welfare expressed in consumption-equivalent units: - CE = exp[(1−γ)(W_P − W^*)]^{−1}. (18) - CE'_0 = exp[(1−β)(W_P − W'^*)]^{−1}. (19) - Positive CE indicates a welfare gain relative to the baseline (policy not active). - For passive policy, both stochastic (second-order) and deterministic models are considered to separate volatility effects from steady-state changes. ### Key findings summarized from model results and policy comparison - Macroprudential tools (changes in collateral requirement z) reduce credit volatility and improve financial stability by lowering the volatility of borrowing. - Complete information case: - Active, countercyclical, time-varying policies are preferred to passive permanent tightening. - Active policies achieve greater financial stability without long-run output costs. - Incomplete information case (indicators observed with noise and lag): - The effectiveness of aggressive active responses is diminished. - A more cautious (less aggressive) active response, or even a passive approach, may be preferable despite the passive approach’s steady-state output cost. - Passive policy trade-offs: - Improves financial stability but implies a permanently lower steady-state output. - The output cost is unevenly distributed across agents and increases inequality. - Policy implication: improving data quality and supervisory capacity to reduce information lags and noise makes active time-varying macroprudential policies more desirable; absent such improvements, cautious responses or considered passive tightening can be warranted, acknowledging output and distributional costs. *Source: wp1759 - 2. The Model8 (IMF Working Paper).* ### 2.6 Macroprudential Policy Alternatives ### 2.6 Macroprudential Policy Alternatives ### Active Policy: A Macroprudential Rule (Collateral requirement rule) - Rule form (complete information): - z_t = z_SS * (E_t b_{t+1} / b_SS)^{φ_b} (equation (B1) described in text) - z_SS is the steady-state value for the collateral requirement. - φ_b ≥ 0 measures the response of the collateral requirement to expected deviations of credit from its steady state. - Policy implication: countercyclical — higher requirements during credit booms; restricts loans and mitigates the credit cycle. - Implementation note: this policy does not imply a change in the steady state of the economy when implemented. - Rule form (incomplete information): - Policymaker observes credit with a lag of four quarters and with error: b_{t-4} = e b_{t-4} + x_t. - Operational rule used in the paper: - z_t = z_SS * [ (b_{t-4} - x_t) / b_SS ]^{φ_b} (equation (20) described in text) - Noise specification: - x_t = ρ_x x_{t-1} + v_t (AR(1) process; equation (21)) - v_t ~ i.i.d. N(0, σ_v^2) - Key implementation risk: noisy and lagged data can trigger unwarranted or ineffective policy responses and introduce further volatility. - Conjectured information problem: policy authority reacts to noise processes (Orphanides (2003) reference). ### Passive Policy - Definition: - Permanent change in the collateral requirement (z) as a non–time-varying macroprudential instrument. - Implementation rationale: - Simpler for LIDCs due to lower data and capacity requirements. - Macro implications: - Changes the economy’s steady state (permanent restriction of credit). - Example qualitative outcome: permanent increase in collateral reduces steady-state credit and steady-state output — entails a long-run output cost. ### Dynamic Properties — Parameter Values (Benchmark Calibration) - Benchmark calibration values (Table 1): - β Discount Factor Households: 0.99 - γ Discount Factor Entrepreneurs: 0.98 - z Collateral Requirement: 183.2 - δ Capital depreciation: 0.03 - μ Capital Share: 0.35 - η Labor supply: 3 - ρ Shock persistence: 0.8 - Notes on calibration: - Collateral benchmark from World Bank Enterprise Survey Data: in Sub-Saharan Africa the value of collateral needed for a loan is 183.2%. - Discount factor for households set to 0.99 (annualized interest ≈ 4%). - Entrepreneur discount factor slightly lower to make collateral constraint binding. - Demand shock: additive shock "t in Euler equation; log("t) follows AR(1) with persistence set to 0.80. ### Impulse Responses — Key Quantitative Findings - Setup for comparisons: - Three cases: benchmark (no macroprudential policy), active rule with complete information, passive policy calibrated to match average increase implied by active rule. - Active rule reaction parameter used for presentation: φ_b = 0.5 (complete information). - Passive rule calibrated by taking average increase of the collateral requirement implied by active rule for first 20 periods and approximating a permanent equivalent increase. - Example: benchmark collateral requirement 183.2 increases to approximately 250 in the passive calibration (text: "In the benchmark case, it is an increase in the requirement from 183.2 to 250, approximately."). - Qualitative impulse-response results to a positive demand shock: - Active rule (complete information): - Collateral requirements increase temporarily and return to the steady state as shock passes. - Cuts borrowing more strongly than passive rule; mitigates expansion in entrepreneurial consumption. - Household consumption increases less (they save less due to cut in credit). - Interest rate decreases more with a macroprudential tool (interest rate inversely related to collateral requirement). - No long-run output cost (steady state of output unchanged). - Passive rule: - Collateral requirement increases permanently, achieving credit compression but reducing steady-state credit and output — long-run output cost. - Benchmark (no macroprudential): - Collateral requirement remains at steady-state level 183.2 through the shock. ### Macroeconomic and Financial Effects - Active Policy with Complete Information — Financial stability vs. reaction parameter φ_b: - Standard deviation of borrowing used as proxy for financial stability. - Finding: larger φ_b reduces borrowing volatility, but marginal gains diminish at high φ_b. - Numerical examples reported: - φ_b = 100 → standard deviation of borrowing = 0.423537 - φ_b = 1000 → standard deviation of borrowing = 0.421284 - Policy choice in the paper: φ_b = 0.5 selected as a conservative value, not too far from monetary Taylor-rule literature references. - Active Policy with Incomplete Information — Effects of lagged and noisy data: - In experiments the authors used a 1% shock in the data noise with 0.8 persistence (benchmark for noise). - Three incomplete-information cases analyzed: - (i) variables observed with a lag, - (ii) variables observed with noise, - (iii) lagged and noisy data combined. - Main findings: - For very low φ_b, results under complete and incomplete information are similar — cautious implementation reduces sensitivity to information problems. - Aggressive φ_b that is effective under complete information can be counterproductive under incomplete information and increase credit volatility. - Lag alone: rule performs marginally worse than complete information. - Noise alone: rule is less effective and can worsen financial stability compared with complete information. - Lag + noise: exacerbates instability; the macroprudential regulator can generate more instability than the no-policy case when φ_b is large. - Cautious rule benchmark: φ_b = 0.1 yields limited adverse effects under incomplete information (referred to as "cautious rule under incomplete information"). - Conclusion: incomplete information can reverse the stabilizing effects of an active rule if the rule is aggressive; caution and lower φ_b reduce this risk. - Passive Policy — Financial stability tradeoff - Figure 5 (described in text) shows increasing collateral requirements (passive policy) and the implied financial stability (stdev(b)). - Qualitative conclusion: passive policy dampens short-term credit dynamics but reduces steady-state credit and output — a long-run output cost. *Source: "2.6 Macroprudential Policy Alternatives" (wp1759) from the supplied IMF PDF content.* ### 4.3 Passive Policy ### 4.3 Passive Policy ### Overview and mechanism - Passive macroprudential policy in this section is implemented as a permanent increase in the collateral requirement (collateral constraint becomes tighter once and for all). - Intended effect: improve financial stability by reducing the volatility of borrowing; unintended effect: reduce steady-state credit and steady-state output permanently. ### Financial stability effects - Initial calibrated collateral: 183.2%. - Empirical result: "When collateral requirements increase, the standard deviation of credit decreases–a passive macroprudential policy is able to achieve a higher financial stability." (Figure 5 referenced in text.) - To obtain the same financial stability as the active rule (complete information), the collateral requirement would have to be raised permanently to 833 percent, which would imply: - steady-state output = 1.74 - an output loss of 5.1 percent ### Steady-state and distributional effects - Permanent increase in collateral requirement implies: - Lower steady-state level of output (Figure 6). - Reduced access to financial markets for entrepreneurs, lowering borrowing and production in steady state. - Consumption and inequality: - Entrepreneurs have a lower level of consumption in steady state than households; the gap widens under the passive policy (Figure 7). - Gini coefficient increases with higher collateral requirements (Figure 8): "As collateral requirements increase, the Gini coe¢cient becomes larger, meaning that inequality goes up." - Simplified Gini calculation used: if high income group is u% of population and earns a fraction f% of all income, then Gini = f − u (text). - Model calibration adjusted the proportion of entrepreneurs (borrowers) to match the initial Gini coefficient close to the average value in LIDCs. ### Welfare implications - General pattern: - Entrepreneurs benefit from increased financial stability (their consumption volatility falls because entrepreneurial consumption is determined by loans under a binding collateral constraint). - Savers (households) are worse off with the passive policy because their consumption does not depend on financial stability and they face the long-run output cost. - Aggregate welfare: stochastic-model aggregate welfare is positive for some passive-policy parameter values (Figure 12), while deterministic (steady-state) welfare shows entrepreneurs worse off and households slightly better off (Figure 13). - Deterministic (steady-state) decomposition: - Passive policy: entrepreneurs lose (lower steady-state consumption), households gain slightly, aggregate welfare is slightly increasing due to redistribution. ### Comparison with active policy and incomplete information - Active policy (time-varying rule responding to expected deviations of credit) is preferred when the policymaker has complete, timely, and accurate information: - Active rule (complete information) achieves lower variability of borrowing and output without a long-run steady-state cost. - Under incomplete information (noisy and/or lagged data): - Active rule can be welfare-decreasing and generate higher volatility (figure 11, figure 14 discussion). - A more cautious active rule (reaction parameter = 0.1, "cautious rule") or a passive approach may be preferable for the objective of attaining low variability of credit and output, despite long-run output cost and distributional consequences. - For the "cautious rule," the active rule is preferred to the passive rule up to a collateral requirement of approximately 312 percent. - Quantitative caution: "Quantitative results should be taken with some caution since the rule is not optimally implemented and the value of the noise is not calibrated to a specific case." ### Quantitative summary (selected reported statistics) - Table 2: Volatilities and steady states (columns: Benchmark | Active (Complete Inf ) | Active (Incomplete Inf ) | Passive) - σ_b: 6.31 | 2.91 | 13.72 | 5.15 - σ_y: 2.69 | 1.72 | 3.56 | 2.17 - b_SS: 8.75 | 8.75 | 8.75 | 6.03 - y_SS: 1.83 | 1.83 | 1.83 | 1.80 - Illustration from text: to match active rule (complete information) financial stability, passive collateral → 833 percent → steady-state output 1.74 (output loss of 5.1 percent). - Table 3: Welfare and inequality (columns: Benchmark | Active (Complete) | Active (Incomplete) | Passive) - Welfare gain: -0.38 | -0.99 | 0.22 | (passive column as presented in source) - c_SS (entrepreneur consumption steady state): 0.19 | 0.19 | 0.19 | 0.15 - c0_SS (household consumption steady state): 6.34 | 6.34 | 6.34 | 6.53 - Gini: 0.46 | 0.46 | 0.46 | 0.48 ### Policy trade-offs and recommendations - Trade-offs: - Passive policy: improves financial stability (lower credit volatility) but imposes a permanent steady-state output cost and raises inequality by disproportionately reducing entrepreneurs’ consumption. - Active policy (complete information): preferred—achieves lower volatility without steady-state cost. - Active policy (incomplete information): can be counterproductive—higher volatility and welfare losses; a cautious active rule or passive approach can be preferable under noisy/lagged data. - Recommendations for LIDCs: - Be cautious in adopting passive macroprudential tools as a first-best response due to long-run output, inequality, and welfare implications that may outweigh stability benefits. - Prioritize reducing data and capacity problems, and improving policy framework and implementation, to enable effective use of time-varying (active) macroprudential approaches. - As data and monitoring improve, consider less aggressive responses to financial sector developments. *Source: wp1759 - 4.3 Passive Policy (IMF working paper content provided).* ### References ### References ### Monetary policy, macroprudential policy, and banking - [1] Angelini, P., Neri, S., Panetta, F., (2014), The Interaction between Capital Requirements and Monetary Policy, Journal of Money, Credit and Banking, 46 (6) - [2] Angeloni, I., Faia, E., (2013) ‘Capital regulation and monetary policy with fragile banks.’ Journal of Monetary Economics 60 (3), pp. 311—324 - [4] Arregui, N., Beneö, J., Krznar, I., Mitra, S„ and Oliveira Santos A., (2013), Evaluating the Net Benefits of Macroprudential Policy: A Cookbook, IMF Working Paper 13/167 - [9] Benigno, P., Woodford, M., (2008), Linear-Quadratic Approximation of Optimal Policy Problems, mimeo - [17] IMF (2014) (b), Sta§Guidance Note on Macroprudential Policy, IMF Sta§Papers - [23] Masson, P., (2014), Macroprudential Policies, Commodity Prices and Capital Inflows, Bis Paper 76 - [30] Rubio, M., Carrasco-Gallego, J.A., (2014), "Macroprudential and monetary policies: Implications for financial stability and welfare," Journal of Banking & Finance, Elsevier, vol. 49 (C), pp. 326-336 - [33] Unsal, D. F., (2013), "Capital Flows and Financial Stability: Monetary Policy and Macroprudential Responses," International Journal of Central Banking, 9(1), pp. 233-285 ### Monetary policy design, rules, and evaluation - [3] Aoki, Kosuke (2003), "On the optimal monetary policy response to noisy indicators," Journal of Monetary Economics, Vol. 50, pp. 501—523 - [25] McCallum (2001), "Should Monetary Policy Respond Strongly to Output Gaps?," American Economic Review, 91(2), pp. 258-262 - [27] Orphanides, Attanasios (2003), "Monetary Policy Evaluation With Noisy Information," Journal of Monetary Economics, Vol. 50, No. 3, pp. 605—631 - [29] Rabanal, P., (2004), Monetary Policy Rules and the U.S. Business Cycle: Evidence and Implications, IMF Working Paper WP/04/164 - [31] Schmitt-Grohe, S., Uribe, M., (2004), "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Journal of Economic Dynamics and Control, 28, 755-775 - [32] Schmitt-Grohé, S., Uribe, M., (2007), "Optimal simple and implementable monetary and fiscal rules," Journal of Monetary Economics 54, pp. 702—1725 - [26] Monacelli, T., (2006), "Optimal Monetary Policy with Collateralized Household Debt and Borrowing Constraint," in conference proceedings "Monetary Policy and Asset Prices" edited by J. Campbell ### Credit, housing, and financial accelerator literature - [10] Bernanke, B. S., Gertler, M., and Gilchrist, S., (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework,” Handbook of Macroeconomics, ed. J. B. Taylor and M.Woodford, Vol. 1C, pp. 1341—93 - [14] Iacoviello, M., (2005), “House Prices, Borrowing Constraints and Monetary Policy in the Business Cycle,” American Economic Review, Vol. 95 (3), pp. 739-764. - [15] Iacoviello, M., Minetti, R., (2006), “International Business Cycles with Domestic and Foreign Lenders,” Journal of Monetary Economics, Vol. 53, No. 8, pp. 2267-2282 - [20] Kiyotaki, N., Moore, J., (1997), “Credit Cycles.” Journal of Political Economy, 105(2), pp. 211—48 - [24] Mendicino, C., Pescatori, A., (2007), Credit Frictions, Housing Prices and Optimal Monetary Policy Rules, mimeo - [19] Kannan, P., Rabanal, P., Scott, A.M., (2012), Monetary and Macroprudential Policy Rules in a Model with House Price Booms, The B.E. Journal of Macroeconomics, 12 (1) - [22] Martinez, J., Rabanal, O., Unsal, D.F., “Credit Markets and Macroprudential Policy in Low-Income and Developing Countries”, forthcoming IMF working paper. ### Modeling, welfare, and DSGE approaches - [5] Ascari, G., Ropele, T., (2009), Disinflation in a DSGE Perspective: Sacrifice Ratio or Welfare Gain Ratio?, Kiel Institute for the World Economy Working Paper, 1499 - [7] Baldini, A., Beneö, J., Berg, A., Dao, M. C., and Portillo, R., (2015), "Monetary Policy in Low Income Countries in the Face of the Global Crisis: A Structural Analysis," Pacific Economic Review 20 (1) - [11] Dabla-Norris, E., Ji, Y., Towsend, R., and Unsal. D.F., Identifying Constraints to Financial Inclu-sion and their Impact on GDP and Inequality: A Structural Framework for Policy, IMF Working Paper, 15/22 - [21] Litchfield, J. (1999)., Inequality: Methods and Tools, The World Bank - [31] Schmitt-Grohe, S., Uribe, M., (2004), "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Journal of Economic Dynamics and Control, 28, 755-775 ### Africa, low-income countries, and financial inclusion - [8] Beck, T., Maimbo, S. M., (2013), Financial Sector Development in Africa, The World Bank - [12] Gottschalk, R., (2014), Institutional Challenges for E§ective Banking Regulation and Supervision in Sub-Saharan Africa, ODI Working Paper 406 - [13] Gri¢th-Jones, S., Gottschalk, R., Spratt, S., (2015), Achieving Financial Stability and Growth in Africa, Routledge book - [16] IMF (2014) (a), Proposed New Grouping in WEO Country Classifications: Low-Income Developing Countries, IMF Policy Paper - [28] Portillo, R., Unsal, D. F., O’Connell, S., Pattillo, C., "Operational Frameworks, Signaling and the Transmission of Monetary Policy in Low-Income Countries," Monetary Policy in Sub-Saharan Africa, Rafael Portillo and Andrew Berg (eds), forthcoming Oxford University Press. ### Inequality, redistribution, and consumption - [6] Attanasio, O., Pistaferri, L., (2016), "Consumption Inequality," Journal of Economic Perspectives, 30 (2), pp. 1—27 - [18] IMF (2014),(c), Redistribution, Inequality, and Growth, IMF Sta§Discussion Note - [22] Martinez, J., Rabanal, O., Unsal, D.F., “Credit Markets and Macroprudential Policy in Low-Income and Developing Countries”, forthcoming IMF working paper. *Source: wp1759 - References (IMF working paper references list)* --- _Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1759.pdf_